Schemes of interchangeable windings of electrical machines

ABSTRACT

Winding diagrams, in which there is no intersection of endwindings in space and which are suitable for interchangeable windings of electrical machines, are considered in the proposed invention. Winding diagrams of a three-phase, two-layer concentric winding with a 120° phase zone and a three-phase, three-layer concentric winding with a 180° phase zone are considered. The scheme of a three-phase two-layer concentric winding with 120° phase with a linear distribution of turns in phase coils is offered for improvement of MMF distribution. The scheme of a three-phase, three-layer concentric winding with 180° phase zone with trapezoidal distribution of turns in phase coils is also proposed for improvement of MMF distribution.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is divisional of application Ser. No. 12/355,858 filed Jan. 19, 2009.

FIELD OF INVENTION

This invention is related to the field of electrical engineering, to the field of electrical machines and in particular to the field of winding diagrams of electrical machines.

BACKGROUND OF INVENTION

A production technology of interchangeable windings of electrical machines is described in US 20100181860. In accordance with the specified technology, windings of electrical machines are made outside the stator (FIG. 1). Such a winding represents a solid body with strictly determined geometrical shape and strictly determined physical properties, such as a number of phases, a number of slots, a number of poles, a number of coils per phase, an applied winding diagram, a number of layers within the winding, wire diameter, active resistance and inductive resistance of a phase (FIG. 2). A winding manufactured in accordance with the specified technology is simply inserted or pressed into a stator (FIG. 3, 4).

Preliminary investigations have shown that windings of electrical machines of alternating current with 120° and 180° phase zones manufactured in accordance with the above mentioned technology have more compact endwindings, than traditional windings of electrical machines with a 60° phase zone. Investigations have also revealed that windings having no intersections of endwindings are more suitable for the production technology of interchangeable windings of electrical machines.

Most suitable winding diagrams for interchangeable windings of electrical machines are the subject of the present invention.

SUMMARY OF INVENTION

A winding diagram of a three-phase two-layer concentric winding with a 120° phase zone for interchangeable windings of electrical machines of alternating current is proposed in the present invention. There is no intersection of endwindings in such a winding. Each phase of the winding occupies 120 electrical degrees in a single layer. There are three phases, which occupy consistently 360 electrical degrees depending on a number of poles of the winding, in each layer. Coils of one layer have an angular displacement in space of 180 electrical degrees with respect to coils of another layer. The minimum number of slots is equal to 12. If an accordant connection of phase coils is used, the winding diagram represents a winding of a four-pole electrical machine or a winding of an electrical machine with a number of poles, multiple of four. If an anti-parallel connection of phase coils is used, the winding diagram represents a winding of a two poles electrical machine or a winding of an electrical machine with a number of poles, multiple of two.

A winding diagram of a three-phase three-layer concentric winding with a 180° phase zone is also proposed for interchangeable windings of electrical machines. There is also no intersection of endwindings in such a winding. Each phase of the winding occupies one layer. Coils of one layer are displaced in space with respect to coils of another layer by 120 electrical degrees. The minimum number of slots is equal to 12. If an anti-parallel connection of phase-coils is used, the winding diagram represents a winding of a two-pole electrical machine or a winding of an electrical machine with a number of poles, multiple of two. If an accordant connection of phase coils is used, the winding diagram represents a winding of a four-pole electrical machine or a winding of an electrical machine with a number of poles, multiple of four.

If phase EMF needs to be increased and MMF distribution needs to be improved, a winding diagram of a three-phase two-layer concentric winding with a 120° phase zone with a linear distribution of turns in phase coils is offered for interchangeable windings of electrical machines. The sum of turns in each slot of the three-phase winding would remain constant in this case.

Also for the purpose of increase of phase EMF and improvement of MMF distribution, a winding diagram of a three-phase three-layer concentric winding with a 180° phase zone with trapezoidal distribution of turns in phase coils is proposed for interchangeable windings of electrical machines. In this case the sum of turns in the each slot of the three-phase winding would remain constant.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the process of winding of an interchangeable winding of electrical machines.

FIG. 2 shows a manufactured interchangeable winding of electrical machines.

FIG. 3 shows the assembling process of a stator with an interchangeable winding.

FIG. 4 shows a manufactured stator with an interchangeable winding.

FIG. 5 shows a two-pole, three-phase winding with a 120° phase zone.

FIG. 6 shows magnetic field of a two-pole, three-phase winding with a 120° phase zone.

FIG. 7 shows a principle scheme of a two-layer, three-phase winding with concentric coils and with a 120° phase zone.

FIG. 8 shows a winding diagram of a two-layer, three-phase, four-pole winding with concentric coils, with 24 slots and with a 120° phase zone.

FIG. 9 shows magnetic field distribution of a four-pole, three-phase winding with concentric coils and with a 120° phase zone.

FIG. 10 shows a winding diagram of a single phase of a two-layer, three-phase, four-pole winding with concentric coils, with 12 slots, with a 120° phase zone having series and parallel connection of phase coils.

FIG. 11 shows a winding diagram of a single phase of a two-layer, three-phase, two-pole winding with concentric coils, with 12 slots, with a 120° phase zone having series and parallel connection of phase coils.

FIG. 12 shows a principle scheme of a three-layer, three-phase winding with concentric coils, with a 180° phase zone.

FIG. 13 shows a winding diagram of a three-layer, three-phase, four-pole winding with concentric coils, with 24 slots, with a 180° phase zone.

FIG. 14 shows magnetic field distribution of a two-pole, three-phase winding with concentric coils, with 180° phase zone.

FIG. 15 shows a winding diagram of a single phase of a three-layer, three-phase, two-pole winding with concentric coils, with 12 slots, with a 180° phase zone having series and parallel connection of phase coils.

FIG. 16 shows a winding diagram of a single phase of a three-layer, three-phase, four-pole winding with concentric coils, with 12 slots, with a 180° phase zone having series and parallel connection of phase coils.

FIG. 17 shows a principle scheme of a two-layer, three-phase winding with concentric coils, with a 120° phase zone with a linear distribution of turns in concentric coils.

FIG. 18 shows a principle scheme of a three-layer, three-phase winding with concentric coils, with a 180° phase zone with a trapezoidal distribution of turns in concentric coils.

FIG. 19 shows distribution of the total number of turns in slots of a three-layer, three-phase winding with concentric coils, with a 180° phase zone in case of a sinusoidal distribution.

FIG. 20 shows distribution of the total number of turns in slots of a three-layer, three-phase winding with concentric coils, with a 180° phase zone in case of a trapezoidal distribution.

FIG. 21 shows distribution of the total number of turns in slots of a two-layer, three-phase winding with concentric coils, with a 120° phase zone in case of a sinusoidal distribution.

FIG. 22 shows distribution of turns in slots of a two-layer, three-phase winding with concentric coils, with a 120° phase zone in case of a linear distribution.

DETAILED DESCRIPTION

A well-known principle scheme of a two-pole winding with a 120° phase zone and a picture of magnetic field distribution, created by this winding, are presented on FIG. 5 and FIG. 6. In the winding diagram, presented on FIG. 5, one side of coils of a single phase is located in one layer, and other side of coils of this phase is located in another layer. Coils in the given winding can have a diametral pitch or they can represent concentric coils. Anyway, endwindings of the given winding intersect in space. Current in the slots, occupied by coils of a single phase, taking space of 120° electrical degrees, flows in the same direction.

A principle scheme of a two-layer, three-phase alternating current winding with concentric coils and a 120° phase zone, is presented on FIG. 7. A winding diagram of a two-layer three-phase two-pole, concentric winding with a 120° phase zone, is presented on FIG. 8. Unlike in the well-known scheme shown in FIG. 5, coils of a single phase in the presented invention are located in the same layer and connected concentrically (FIG. 8) in the scheme. In a three-phase winding, each phase has two concentric coils, located in different layers. One side of coils of a single phase occupies a half of the phase zone. Another side of these coils is located in the same layer and occupies the second half of the phase zone (FIG. 7, FIG. 8). Phase coils in another layer are connected in a similar manner. For the three-phase electrical machine phase coils occupy a phase zone, which is equal to 120 electrical degrees. As one can see from FIG. 7, 8, current in a half of slots of a concentric coil of a single phase has one direction, and in another half of slots has an opposite direction. The phase coils of a three-phase electrical machine, located in a single layer, are displaced in space with respect to each other by 120 electric degrees (FIG. 7, FIG. 8). The coils of a single phase, located in different layers, are displaced in space by 180 electric degrees. This means that the coils of a single phase, which are situated in different layers, are located opposite to each other. Phase coils consist of concentric coils, connected in series. The beginnings of concentric coils of phases are designated (A1-A3, B1-B3, C1-C3) (FIG. 7). The ends of concentric coils of phases are designated (X1-X3, Y1-Y3, Z1-Z3) (FIG. 7). As one can see from drawings (FIG. 7, FIG. 8), the endwindings of such a winding remain in the same layer.

A winding diagram of a two-layer, three phase, two-pole windings with concentric coils, with 24 slots and a 120° phase zone, is presented on FIG. 8. A picture of magnetic field distribution, created by this winding, is presented on FIG. 9.

In the basic case, this winding diagram gives a four-pole electrical machine (FIG. 10) with a concordant connection of coils of each phase, located in different layers. Such a winding diagram having series and parallel connection of phase coils, located in different layers of the winding, with 12 slots for the whole winding, is presented on FIG. 10. In the basic case this winding diagram gives a two-pole electrical machine (FIG. 11) having counter connection of coils of each phase, located in different layers. A winding diagram for a series and parallel connection of coils of each phase, located in different layers of the winding, is shown on FIG. 11. The input wires of concentric coils of phases are designated (A1 and A2) (FIG. 10, 11). The output wires of concentric coils of phases are designated (X1 and X2) (FIG. 10, 11).

A four-pole winding diagram of the given winding has the maximum winding pitch of

${y_{\max} = {\frac{4}{3}\tau}},$

where τ is a pole pitch. The average winding pitch for the four-pole scheme is equal to

$y_{av} = {\frac{2}{3}{\tau.}}$

The two-pule winding diagram of the given winding has the maximum winding pitch of

$y_{\max} = {\frac{2}{3}{\tau.}}$

The average pitch of the winding for the two-pole winding diagram is equal to

$y_{av} = {\frac{1}{3}{\tau.}}$

It is obvious that the four-pole winding diagram for the given winding is more preferable with respect to efficiency of the use of the winding.

The basic properties of a two-layer, m-phase winding with concentric coils for the two-pole and four-pole winding diagrams are presented in Table 1.

The basic properties of a two-layer, three-phase winding with concentric coils, with 12 slots for the two-pole and four-pole winding diagrams are presented in Table 2.

TABLE 1 Number of layers of winding n, (n = 2) Number of poles 2p = 2k, k = 1, 2, 3, . . . 2p = 4k, k = 1, 2, 3, . . . Number of coils N_(k) = km, where N_(k) = km, where per layer m − numbers of phases m − numbers of phases Number of coils N_(kph) = k N_(kph) = k per layer per phase Total number M_(k) = nmk = 2mk M_(k) = nmk = 2mk of coils Number of coils M_(kph) = 2k M_(kph) = 2k per phase Phase zone for a concentric coil in electrical degrees $\quad\begin{matrix} {\alpha_{w} = \frac{360}{m}} \\ {{{for}\mspace{14mu} m} = {{3\mspace{14mu} \alpha_{w}} = {120{^\circ}}}} \end{matrix}$ $\quad\begin{matrix} {\alpha_{w} = \frac{360}{m}} \\ {{{for}\mspace{14mu} m} = {{3\mspace{14mu} \alpha_{w}} = {120{^\circ}}}} \end{matrix}$ Number of slots Z = 2mki, Z = 2mki, in winding i = 2, 3, 4, . . . i = 2, 3, 4, . . . for m = 3 for m = 3 Z = 12, 18, 24, 30, . . . Z = 12, 18, 24, 30, . . . Number of slots per pole and per phase $\quad\begin{matrix} {q = {\frac{Z}{2\; {pm}} = {\frac{2 \cdot 3 \cdot k \cdot i}{2 \cdot k \cdot 3} = i}}} \\ {{q = 2},3,4,5,\ldots} \end{matrix}$ $\quad{\begin{matrix} {q = {\frac{Z}{2\; {pm}} = {\frac{2 \cdot 3 \cdot k \cdot i}{4 \cdot k \cdot 3} = \frac{i}{2}}}} \\ {{q = 1},\frac{3}{2},2,\frac{5}{2},\ldots} \end{matrix}\quad}$

TABLE 2 Number of layers of winding n = 2, m = 3 Number of poles 2p = 2 2p = 4 Number of coils N_(k) = 3 N_(k) = 3 per layer Number of coils N_(kph) = 1 N_(kph) = 1 per layer per phase Total number M_(k) = 6 M_(k) = 6 of coils Number of coils M_(kph) = 2 M_(kph) = 2 per phase Phase zone for a α_(w) = 120° α_(w) = 120° concentric coil in electrical degrees Number of slots in Z = 2mki, i = 2 Z = 2mki, i = 2 winding Z = 12 Z = 12 Number of slots per pole and per phase $\quad\begin{matrix} {q = {\frac{Z}{2\; {pm}} = {\frac{2 \cdot 3 \cdot k \cdot i}{2 \cdot k \cdot 3} = i}}} \\ {q = 2} \end{matrix}$ $\quad\begin{matrix} {q = {\frac{Z}{2\; {pm}} = {\frac{2 \cdot 3 \cdot k \cdot i}{4 \cdot k \cdot 3} = \frac{i}{2}}}} \\ {q = 1} \end{matrix}$

The principle scheme of a three-layer, three-phase alternating current winding with concentric coils, with a 180° phase zone, is presented on FIG. 12. The winding diagram of a three-layer, three-phase and two-pole, concentric winding with 180° phase zone, is presented on FIG. 13. In accordance with the winding diagram proposed in this invention, the coils of one phase, located in one layer, are connected concentrically (FIG. 13). In a three-phase winding, each phase has two concentric coils, located in one layer. One side of coils of each phase occupies a half of the phase zone, another side of these coils is located in the same layer and occupies the second half of the phase zone (FIG. 13, FIG. 14). Coils of other phases in other layers are connected in the same manner. In case of a three-phase electrical machine, phase coils occupy a phase zone that is equal to 180 electrical degrees. As one can see from FIG. 12, 13, current in a half of slots of a concentric coil of each phase flows in one direction, and in another half of slots flows in the opposite direction. The coils of one phase are located in a single layer. In case of a three-phase electrical machine coils of other phases located in other layers, are displaced in space with respect to each other by 120 electrical degrees (FIG. 13, FIG. 14). Axes of phase coils, located in different layers, are displaced by 120 electrical degrees. Phase coils consist of concentric coils connected in series. The number of layers is equal to the number of phases in the given winding. The input wires of concentric phase coils are designated (A1-A6, B1-B6, C1-C6) (FIG. 12). The output wires of concentric phase coils are designated (X1-X6, Y1-Y6, Z1-Z6) (FIG. 12). As one can see from drawings (FIG. 13, FIG. 14), endwindings of such a winding also remain in the same layer.

A winding diagram of a three-layer, three phase, two-pole windings with concentric coils, with 24 slots and with a 180° phase zone, is presented on FIG. 13. The picture of magnetic field distribution, created by this winding, is presented on FIG. 14.

If coils of each phase located in one winding layer have a counter connection, the winding diagram gives in the basic case a two-pole electrical machine (FIG. 15). The given winding diagram having a series and parallel connection of phase coils, located in one layer of the winding, with 12 slots for the whole winding, is shown on FIG. 15. When phase coils located in one winding layer have a concordant connection, the winding diagram gives in the basic case a four-pole electrical machine (FIG. 16). The considered winding diagram for a series and parallel connection of phase coils, located in one winding layer, is shown on FIG. 16. The input wires of concentric phase coils are designated (A1 and A2) (FIG. 15, 16). The output wires of concentric phase coils are designated (X1 and X2) (FIG. 15, 16).

The two-pole winding diagram of the given winding has the maximum winding pitch of y_(max)=τ, where τ is a pole pitch. The average winding pitch for the two-pole scheme is equal to

$y_{av} = {\frac{1}{2}{\tau.}}$

The four-pole winding diagram of the given winding has the maximum winding pitch of y_(max)=2 τ. The average winding pitch for the four-pole winding diagram is equal to y_(av)=τ. It is obvious that the two-pole winding diagram for the given winding is more preferable as it provides a more efficient use of the winding.

The basic properties of a three-layer, m-phase winding with concentric coils for the two-pole and four-pole winding diagram are presented in Table 3.

TABLE 3 Number fo winding layers n, (n = 3) (m = n = 3) Number of poles 2p = 2k, k = 1, 2, 3, . . . 2p = 4k, k = 1, 2, 3, . . . Number of coils per layer $\quad\begin{matrix} {\quad{{N_{k} = {{\frac{2m}{n}k} = {2k}}},}} \\ {{{{where}\mspace{14mu} m} = {3 - {number}}}\mspace{14mu}} \\ {{of}\mspace{14mu} {phases}} \end{matrix}$ $\quad\begin{matrix} {{N_{k} = {{\frac{2m}{n}k} = {2k}}},} \\ {{{{where}\mspace{14mu} m} = {3 - {number}}}\mspace{14mu}} \\ {{of}\mspace{14mu} {phases}} \end{matrix}$ Number of coils N_(kph) = 2k N_(kph) = 2k per layer per phase Total number of coils $M_{k} = {{n\frac{2m}{n}k} = {2{mk}}}$ $M_{k} = {{n\frac{2m}{n}k} = {2{mk}}}$ Number of coils M_(kph) = 2k M_(kph) = 2k per phase Phase zone of a concentric coil in electrical degrees $\quad\begin{matrix} {\quad{\alpha_{w} = \frac{180n}{m}}} \\ {{{for}\mspace{14mu} m} = {{3\mspace{14mu} \alpha_{w}} = {180{^\circ}}}} \end{matrix}$ $\quad\begin{matrix} {\quad{\alpha_{w} = \frac{180n}{m}}} \\ {{{for}\mspace{14mu} m} = {{3\mspace{14mu} \alpha_{w}} = {180{^\circ}}}} \end{matrix}$ Number of slots Z = 12ki, i = 1, 2, 3, . . . Z = 12ki, i = 1, 2, 3, . . . in winding Z = 12, 24, 36, 48, . . . Z = 12, 24, 36, 48, . . . Number of slots per pole and per phase $\quad\begin{matrix} {q = {\frac{Z}{2\; {pm}} = {\frac{12 \cdot k \cdot i}{2 \cdot k \cdot 3} = {2i}}}} \\ {{q = 2},4,6,\ldots} \end{matrix}$ $\quad{\begin{matrix} {q = {\frac{Z}{2\; {pm}} = {\frac{12 \cdot k \cdot i}{4 \cdot k \cdot 3} = i}}} \\ {{q = 1},2,3,\ldots} \end{matrix}\quad}$

TABLE 4 Number of winding layers n = 3 (m = 3) Number of poles 2p = 2 2p = 4 Number of coils N_(k) = 2 N_(k) = 4 per layer Number of coils N_(kph) = 2 N_(kph) = 2 per layer, per phase Total number of coils M_(k) = 6 M_(k) = 6 Number of coils M_(kph) = 2 M_(kph) = 2 per phase Phase zone of a α_(w) = 180° α_(w) = 180° concentric coil in electrical degrees Number of slots Z = 12ki, i = 1 Z = 12 Z = 12ki, i = 1 Z = 12 in winding Number of slots per pole and per phase $\quad\begin{matrix} {\quad{\quad{q = {\frac{Z}{2\; {pm}} = {\frac{12 \cdot k \cdot i}{2 \cdot k \cdot 3} = {2i}}}}}} \\ {q = 2} \end{matrix}$ $\quad\begin{matrix} {\quad{q = {\frac{Z}{2\; {pm}} = {\frac{12 \cdot k \cdot i}{4 \cdot k \cdot 3} = i}}}} \\ {q = 1} \end{matrix}$

The basic properties of a three-layer, three-phase winding with concentric coils, with 12 slots for the two-pole and four-pole winding diagram are presented in Table 4.

The general properties of offered concentric windings can be described as follows. The total number of coils in the offered winding diagram of concentric windings equals M_(k)=2 pm, where m is the number of phases, and p is the number of pole pairs. The number of coils per layer equals

${N_{k} = \frac{2{pm}}{n}},$

where n is number of winding layers. The number of coils per layer equals N_(k)=2p for windings with a number of layers equals to the number of phases (n=m). The number of coils per layer per phase, equals N_(kph)=2p for windings with a number of layers equal to the number of phases (n=m). The angle in space, occupied by a single concentric winding, equals

$\alpha_{w} = {\frac{360p}{\left( \frac{2{pm}}{n} \right)} = \frac{180}{\left( \frac{m}{n} \right)}}$

electrical degrees. This angle is called a phase zone. Phase coils are displaced from each other in space by the angle, which equals

$\alpha_{coils} = \frac{360}{m}$

electrical degrees.

Number of concentric coils per phase per layer, for a two-layer (n=2), three-phase winding (m=3) (FIG. 7, 8, 10, 11), equals

$n_{coils} = {\frac{Z}{2N_{k}} = {\frac{2{mki}}{2{mk}} = i}}$

where i=2, 3, 4, . . . , (see Table 1).

The maximum winding pitch, for a two-layer (n=2), three-phase winding (m=3) (FIG. 8, 10, 11), equals

$y_{\max} = {{\frac{Z}{mk} - 1} = {{\frac{2{mki}}{mk} - 1} = {{2i} - 1.}}}$

The pitch of coils for a two-layer (n=2), three-phase winding (m=3) (FIG. 8, 10, 11), varies in accordance with the following law

y _(l) =y _(max)−2(l−1),

where l=1, 2, 3, . . . , i is the coil index number.

For example, for a two-layer (n=2), three-phase (m=3), four-pole winding (FIG. 7, 8), having i=3, the maximum winding pitch equals y_(max)=2i−1=2·3−1=5 and the highest coil index number equals l_(max)=i=3:

Coil index number l Pitch y 1 5 2 3 3 1 The coil (A1-X1) has the maximum pitch. The coil (A3-X3) has the minimum pitch (FIG. 7).

Number of concentric coils per phase per layer, for a three-layer (n=3), three-phase winding (m=3) (FIG. 13, 15, 16), equals

${n_{coils} = {\frac{Z}{2N_{k}} = {\frac{12 \cdot k \cdot i}{2 \cdot 2 \cdot k} = {3i}}}},$

where i=1, 2, 3, . . . , (see Table 3).

The maximum winding pitch for a three-layer (n=3), three-phase winding (m=3) (FIG. 13, 15, 16), equals

$y_{\max} = {{\frac{Z}{2k} - 1} = {{\frac{12{ki}}{2k} - 1} = {{6i} - 1.}}}$

The pitch of coils for a three-layer (n=3), three-phase winding (m=3) (FIG. 13, 15, 16), varies according to the law

y _(l) =y _(max)−2(l−1),

where l=1, 2, 3, . . . , 3i is the coil index number. For example, for a three-layer (n=3), three-phase (m=3), two-pole winding (FIG. 13, 15), having i=1, the maximum winding pitch y_(max)=6i−1=6·1−1=5, and the highest coil index number equals l_(max)=3i=3:

Coil index number l Pitch y 1 5 2 3 3 1 For=2, y_(max)=6i−1=6·2−1=11, l_(max)=3i=6:

Coil index number l Pitch y 1 11 2 9 3 7 4 5 5 3 6 1 The coil (A1-X1) has the maximum pitch. The coil (A6-X6) has the minimum pitch (FIG. 12).

It is possible to provide a sinusoidal distribution of turns in the concentric coils of a single phase in order to achieve an improvement of MMF distribution of proposed windings. Principle schemes of sinusoidal distribution of turns in concentric coils for each phase in two-layer and three-layer, three-phase windings are presented on FIG. 17, 18. The input wires of concentric coils of phases are designated (A1-A3) (FIG. 17), (A1-A6) (FIG. 18). The output wires of concentric coils of phases are designated (X1-X3) (FIG. 17), (X1-X6) (FIG. 18). A number of turns in concentric coils w_(coil) changes according to the sinusoidal law with an angular position γ (FIG. 17, 18) of the coil in the stator. For a two-layer concentric winding, the number of turns in concentric coils w_(coil) equals:

$w_{coil} = {{\sin \left( {\frac{\pi}{2} - {\frac{\pi}{\alpha_{w}}\gamma}} \right)}.}$

For a two-layer, three-phase concentric winding (FIG. 17), the number of turns in concentric coils w_(coil) equals:

${w_{coil} = {\sin\left( {\frac{\pi}{2} - {\frac{3}{2}\gamma}} \right)}},$

where the angle γ changes from 0 to 60 electrical degrees. For a three-layer, three-phase concentric winding, the number of turns in concentric coils w_(coil) equals:

${w_{coil} = {\sin \left( {\frac{\pi}{2} - \gamma} \right)}},$

where the angle γ changes from 0 to 90 electrical degrees.

Investigations show that the number of turns and the number of conductors in a slot is not a constant value at sinusoidal distribution of turns in phase coils of two-layer or three-layer three-phase concentric winding (FIG. 19, 21).

For a three-layer, three-phase concentric winding, the number of turns and the number of conductors in slots would be a constant value at trapezoidal distribution of turns in concentric coils of a phase (FIG. 20). The basis of trapezium, where the number of conductors in slots reaches the maximum value, equals to 60 electrical degrees. One coil has only a half of these 60 electrical degrees. So, one coil takes 30 electrical degrees. When the angle γ varies from 30 to 90 electrical degrees, a distribution of turns in concentric coils of a phase changes according to the linear law: from the maximum value down to zero at the infinite number of slots in the winding or down to the minimum value at a finite number of slots in the winding. The number of concentric coils per phase for such a winding equals n_(coils)=3i. The phase zone of such a winding equals 180 electrical degrees. So, a half of coils of a single phase takes 90 electrical degrees. Then we need to have i coils on 30 electrical degrees. Thus, when the angle γ varies from 0 to 30 electrical degrees, the number of turns in i coils is the maximum and the constant. Consequently, the pitch of these coils changes from the maximum y_(max)=6i−1 to a pitch equal to y_(l=i)=y_(max)−2(i−1). The number of turns changes from maximum to the minimum value according to the linear law for the further change of the angle γ from 30 to 90 electrical degrees in the rest of 2i coils. Thus the pitch of these coils changes from a pitch equal to y_(i=i+1)=y_(max)−2i, down to the minimum pitch equal to 1. The total number of turns and conductors in each slot of the winding is constant (FIG. 20) at the specified distribution of turns in concentric phase coils.

The number of turns and the number of conductors in slots would be a constant value at a linear distribution of turns in concentric phase coils (FIG. 22) for a two-layer, three-phase concentric winding. When the angle γ varies from 0 to 60 electrical degrees the number of turns in concentric coils of a phase changes from the maximum value at the coil having the maximum pitch y_(max), down to the minimum value at the coil having minimum pitch equal to 1. The total number of turns and conductors in each slot of the winding is constant (FIG. 22) at the specified distribution of turns in concentric phase coils.

The proposed windings could be also applied for conventional electrical machines. Absence of intersection of endwindings can considerably improve the quality of the plunger technology used for mounting windings.

A two-layer, three-phase concentric winding with linear distribution of turns in concentric phase coils has improved MMF distribution and could be applied for electrical machines used in high-precision electrical drives.

A three-layer, three-phase concentric winding with trapezoidal distribution of turns in the concentric phase coils has improved MMF distribution and could also be applied for the electrical machines used in high-precision electrical drives. 

1. A two-layer, m-phase winding of electrical machine of alternating current with concentric coils comprising the following combination of properties: a) coils of each phase situated in different layers of the winding, can be connected in series or in parallel so that electric current flowing through these coils would create magnetic field either having the number of poles of 2p=2k or of 2p=4k, where k=1, 2, 3, . . . ; b) the total number of coils equals 2mk; c) the number of coils in one layer of the winding equals mk; d) the number of coils in one layer of the winding, belonging to each phase, equals k; e) the number of coils of the winding, belonging to each phase, equals 2k; f) the phase coils situated in one layer of the winding, are displaced with respect to each other on the angle equal to $\frac{360}{m}$  electrical degrees; g) the phase coils situated in different layers of the winding, are displaced with respect to each other on the angle equal to 180 electrical degrees; h) the phase zone of each coil equals $\frac{360}{m}$  electrical degrees; i) the phase zone includes one coil, consisting of i concentric coils connected in series and having equal number of turns; j) the number of slots in the winding equals Z=2mki, where i=2, 3, 4, . . . is the number of concentric coils in a phase coil; k) the pitch of concentric coils of the phase changes from the maximum, equal to y_(max)=2i−1, down to the minimum, equal 1, under the law y_(l)=y_(max)−2(l−1), where l=1, 2, 3, . . . i; l) the endwindings of coils of different phases and different layers remain in a single layer.
 2. A three-layer, three-phase winding of electrical machine of alternating current with concentric coils comprising the following combination of properties: a) the number of layers equals to the number of phases; b) coils of each phase situated in different layers of the winding, can be connected in series or in parallel so that electric current flowing through these coils would create magnetic field either having a number of poles of 2p=2k or of 2p=4k, where k=1, 2, 3, . . . ; c) the total number of coils equals 6k; d) the number of coils in one layer of the winding equals 2k; e) the number of coils in one layer of the winding, belonging to each phase, equals 2k; f) the coils of one phase are situated only in one layer of the winding; g) the coils of phase, which are situated in different layers of the winding, are displaced with respect to each other on the angle equal to 120 electrical degrees; h) the phase zone of each coil equals 180 electrical degrees; i) the phase zone includes one coil, consisting of 3i concentric coils connected in series and having equal number of turns; j) the number of slots in the winding equals Z=12ki, where i=1, 2, 3, . . . is the number of concentric coils in a phase coil; k) the pitch of concentric coils of the phase changes from the maximum, equal to y_(max)=6i−1, down to the minimum, equal to 1, according to the following law: y_(i)=y_(max)−2(l−1), where l=1, 2, 3, . . . 3i; l) the endwindings of coils of different phases and different layers remain in a single layer.
 3. The winding, according to claim 1, in which the number of turns in concentric coils of phases changes according to the linear law from the maximum number of turns at the concentric coil having the maximum pitch, equal to y_(max)=2i−1, down to the minimum number of turns at the concentric coil having the minimum pitch, equal to 1, thereat the total number of turns and conductors in each slot of the winding is a constant value.
 4. The winding, according to claim 2, in which the number of turns in concentric coils of phases changes according to the trapezoidal law, where in i concentric coils the pitch changes from the maximum equal to y_(max)=6i−1 down to the pitch equal to y_(l=i)=y_(max)−2(i−1) and the number of turns is maximal and constant, in the other 2i concentric coils where the pitch changes from pitch equal to y_(l=i+1)=y_(max)−2 down to the minimum pitch, equal to 1, the number of turns changes according to the linear law from the maximum number of turns down to the minimum number of turns, thereat the total number of turns and conductors in each slot of the winding is a constant value. 